Influence of Parametric Symmetry on the Dynamics of 3D Sinusoidal Discrete Systems

Abstract

The discrete system serves an important role in mimicking collective dynamics found in continuous dynamical systems, which are relevant to many realistic natural and artificial systems. To investigate the dynamical transition of a discrete system, we employ three-dimensional sinusoidal discrete maps with an additional self feedback factor. Specifically, we focus on dynamical transitions with respect to the bifurcation parameter, sine function amplitude, and intensity of self feedback factors. We demonstrate the presence of symmetry in relation to parametric variation using two parameter diagrams. The study is then expanded to the network of sine maps in the presence of self-feedback factor. We discover that negative feedback exhibits the transition from cluster state to synchronization while raising the coupling strength for small-world network interactions. Furthermore, increasing feedback from negative to positive causes the transition from synchronization to desynchronization via chimera state for various complex network connectivities.